Liberal Democrat leader Vince Cable during a question and answer session at the party’s Bournemouth conference. Photo: Andrew Matthews/PA Wire/PA Images

Above the entrance to the Bournemouth conference centre is a video advert for an upcoming show by Squeeze, the 80s band. As the Liberal Democrats gather beneath it, this reminder of the party’s fate at the 2017 general election, as the electorate divided between Labour and the Conservatives, could be making them wince. But instead the Lib Dems, ever the unnatural optimists, are pretty chirpy.

The delegates are pleased with Vince, their new leader. And the party’s unity on the major issue of the day provides a warm, comforting feeling. On the beach, someone has scrawled “EXIT BREXIT” into the sand in giant capital letters—you can read it from the promenade. There are ladies wearing blue berets decorated with the stars of the European flag, and a lot of sagacious nodding about, as Cable put it over the weekend, the “appalling treatment” of EU nationals.

But being the unashamedly anti-Brexit party is both a welcome opportunity for the Lib Dems, rebuilding after a second electoral pummelling this June, and, potentially, a bit of a trap.

An increase in parliamentary seats from eight to 12 (and three very near misses), cannot conceal the underlying trend, which is for the Lib Dem share of the vote to be stuck in single figures—this has been the case ever since Nick Clegg decided to campaign as the anti-Farage in the European election of 2014.

Longtime party strategists worry that there can only be a future for the UK-wide third party if it develops a broader appeal—a core vote up at 20 or even slightly more. This means thinking more systematically ab…

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